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May 4th, 2009, 02:02 PM  #1 
Newbie Joined: Mar 2009 Posts: 9 Thanks: 0  Finding the minimal polynomial
if f = x^3 + 2X+1 is the minimal polynomial of alpha, then what is the minimal polynomial of alpha^2? I have no idea how to solve that. A hint pls. 
May 9th, 2009, 10:24 PM  #2 
Senior Member Joined: Jul 2008 Posts: 144 Thanks: 0  Re: Finding the minimal polynomial
It's impossible, I think.

May 10th, 2009, 12:33 AM  #3  
Member Joined: Aug 2008 Posts: 84 Thanks: 0  Re: Finding the minimal polynomial Quote:
 
May 15th, 2009, 09:56 AM  #4 
Newbie Joined: Mar 2009 Posts: 9 Thanks: 0  Re: Finding the minimal polynomial
Thanks for the replies but I solved the problem myself by looking at the powers of alpha^2. alpha^n can always be written as lin. combination of elements of the basis {0,alpha,alpha^2} if I do so, then I see that a^6 is a linear combination of 1,a^2,a^4 and so by solving the resulting linear equations I found the minimal polynomial. 

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